The symmetries of the sign-changing components \(w_{m+1},\ldots ,w_\ell \)  are basically the same as those considered in [1]}. So one may wonder whether one can obtain a similar result for \(N=5\)  using the symmetries introduced in [2]} or [3]}. As we shall see, this is not possible. A key role is played by the space of fixed points of the group of symmetries involved, see Theorem REF .
